Within minutes of accepting the resignation of Veterans Affairs Secretary Eric K. Shinseki, President Obama and some of his supporters in Congress signaled that their next goal may be a boost in funding for the troubled department’s health care services.

But veterans groups say the problems at the department are with management and leadership, which can’t be fixed with cash.

“Money is not the issue right now,” said Joe Davis, a spokesman for Veterans of Foreign Wars. “It’s honesty in the ranks, identifying and fixing what’s broken, holding people accountable and restoring the faith veterans are supposed to have in their VA.”

He said the department came to Congress at one point asking for money to hire 2,000 more full-time employees, but once these workers were trained and on the job, the number of claims processed per employee went down.

“So the money and full-time employee thing doesn’t work anymore. You got to remember, this is the second-largest line in the budget,” Mr. Burr told The Washington Times in an interview last month. “You could make a tremendous case this is not money and it’s not personnel.”

He insisted that it will take a change in culture and leadership to effect real change.

Still, Mr. Obama and others expect money to be part of the equation for fostering change.

“My suspicion is that with not only all the veterans from Iraq and Afghanistan coming back, but also the aging of our Vietnam vets who may have more chronic illnesses, may need more visits, we may need to get more doctors and we may need to get more nurses,” Mr. Obama said Friday when accepting Mr. Shinseki’s resignation. “That’s going to cost some money.”

Douglas Holtz-Eakin, president of the American Action Forum and former director of the Congressional Budget Office, said money may be able to help in some areas but can’t solve problems of excessive red tape and poor management.

“This is an agency that is synonymous with backlogs, things on paper that should be computerized, terrible management, unresponsiveness,” he said. “Those are not money problems; those are fundamental management issues.”

Sen. Bernard Sanders, Vermont independent and chairman of the Senate Veterans’ Affairs Committee, said he is working on a bill to reform the VA that will include additional spending for health care services and military pensions. The boost in military pensions alone would cost an additional $21 billion over the next decade — a price tag that helped doom the measure in an earlier Senate vote.

In a sharp exchange with Sen. Marco Rubio, Florida Republican, several weeks ago, Mr. Sanders said Republicans must be prepared to pay more to take care of veterans.

“If you think it’s too expensive to take care of our veterans, then don’t send them to war,” Mr. Sanders said during the floor debate.

Peter Gaytan, executive director of the American Legion in Washington, said officials should start thinking about the VA budget only after they have fixed issues with management that “have nothing to do with money.”

“If, during investigations, they find delays are due to an inadequate number of practitioners, that’s when you start talking about more money for full-time employees,” Mr. Gaytan said.

Mr. Holtz-Eakin said he doesn’t believe an increased budget would solve a doctor shortage either because it’s a problem facing the entire medical system.

Some veterans say VA underfunding is not the fault of Congress but rather the fault of the president for underestimating VA needs, said Alex Nicholson, legislative director for Iraq and Afghanistan Veterans of America.

“Congress has given the VA every penny that it and the administration has asked for to fund the VA. So Congress, for once, is not to blame.

“That’s not to say that the VA isn’t underresourced. But if that’s the case, and we still think it is, it’s because the administration has lowballed its budget requests and has not been honest with Congress about what sums are really needed to do what the VA needs to do,” Mr. Nicholson said.